Modification of Parachute Canopy Stiffness Scaling Laws for Opening Time Prediction

Abstract

Nomenclature a = acoustic speed C eff = effective porosity of fabric D, D o = parachute constructed diameter or characteristic dimension D max = maximum open mouth diameter in hang test D z = suspension line damping factor; dD o ∕m l V s d = diameter of fabric yarns, or suspension line damping coefficient E = elastic modulus of fabric EI = flexural rigidity of canopy e c = nondimensional canopy rigidity; EI∕ρV 2 D 4 e s = nondimensional suspension line elasticity; k∕ρV 2 D F p = peak force on payload F r = Froude number; V 2 s ∕gD F z = suspension line elastic factor; kD 2 o ∕m l V 2 s g = acceleration due to gravity K p = parachute spring constant k = suspension line spring constant M = Mach number; V∕a M r;l = mass ratio based on payload mass; m l ∕ρD 3 M r;p = mass ratio based on parachute mass (canopy and lines); m p ∕ρD 3 M r;T = mass ratio based on total system mass; m T ∕ρD 3 m l = payload mass m p = parachute mass (canopy and lines) m T = total system mass q s = dynamic pressure at parachute snatch; 1∕2ρV 2 s R = canopy Reynolds number; ρVD∕μ R f = fabric Reynolds number based on yarn diameter; ρVd∕μ S = canopy projected area t = thickness of fabric, or canopy opening time t f = filling time of canopy V = velocity V s = snatch velocity W c = weight of canopy w cl = weight per unit area of fabric X p = nondimensional opening shock; F p ∕m l g β o = semiaperture angle between suspension lines γ o = initial trajectory angle ζ = effective stiffness index of parachute η = canopy stiffness index μ = dynamic viscosity of air ν = Poisson's ratio of fabric ρ = air density σ = modified stiffness index τ = nondimensional opening time; V s t∕D τ f = nondimensional filling time; V s t f ∕D